Problem: Nauuo is a girl who loves playing chess.

One day she invented a game by herself which needs n chess pieces to play on a m× m chessboard. The rows and columns are numbered from 1 to m. We denote a cell on the intersection of the r-th row and c-th column as (r,c).

The game's goal is to place n chess pieces numbered from 1 to n on the chessboard, the i-th piece lies on (r_i,\,c_i), while the following rule is satisfied: for all pairs of pieces i and j, |r_i-r_j|+|c_i-c_j|≥|i-j|. Here |x| means the absolute value of x.

However, Nauuo discovered that sometimes she couldn't find a solution because the chessboard was too small.

She wants to find the smallest chessboard on which she can put n pieces according to the rules.

She also wonders how to place the pieces on such a chessboard. Can you help her?

Input

The only line contains a single integer n (1≤ n≤ 1000) — the number of chess pieces for the game.

Output

The first line contains a single integer — the minimum value of m, where m is the length of sides of the suitable chessboard.

The i-th of the next n lines contains two integers r_i and c_i (1≤ r_i,c_i≤ m) — the coordinates of the i-th chess piece.

If there are multiple answers, print any.

Examples

Input


2


Output


2
1 1
1 2

Input


4


Output


3
1 1
1 3
3 1
3 3

Note

In the first example, you can't place the two pieces on a 1×1 chessboard without breaking the rule. But you can place two pieces on a 2×2 chessboard like this:

<image>

In the second example, you can't place four pieces on a 2×2 chessboard without breaking the rule. For example, if you place the pieces like this:

<image>

then |r_1-r_3|+|c_1-c_3|=|1-2|+|1-1|=1, |1-3|=2, 1<2; and |r_1-r_4|+|c_1-c_4|=|1-2|+|1-2|=2, |1-4|=3, 2<3. It doesn't satisfy the rule.

However, on a 3×3 chessboard, you can place four pieces like this:

<image>

Solution (in JAVA):

Solution:
import java.io.*;
import java.util.*;
import java.text.*;
import java.math.*;
import java.util.regex.*;

public class Solution 
{
	static class InputReader
	{
	    private final InputStream stream;
	    private final byte[] buf = new byte[8192];
	    private int curChar, snumChars;

	    public InputReader(InputStream st) {
	      this.stream = st;
	    }

	    public int read() {
	      if (snumChars == -1)
	        throw new InputMismatchException();
	      if (curChar >= snumChars) {
	        curChar = 0;
	        try {
	          snumChars = stream.read(buf);
	        } catch (IOException e) {
	          throw new InputMismatchException();
	        }
	        if (snumChars <= 0)
	          return -1;
	      }
	      return buf[curChar++];
	    }

	    public int nextInt() {
	      int c = read();
	      while (isSpaceChar(c)) {
	        c = read();
	      }
	      int sgn = 1;
	      if (c == '-') {
	        sgn = -1;
	        c = read();
	      }
	      int res = 0;
	      do {
	        res *= 10;
	        res += c - '0';
	        c = read();
	      } while (!isSpaceChar(c));
	      return res * sgn;
	    }

	    public long nextLong() {
	      int c = read();
	      while (isSpaceChar(c)) {
	        c = read();
	      }
	      int sgn = 1;
	      if (c == '-') {
	        sgn = -1;
	        c = read();
	      }
	      long res = 0;
	      do {
	        res *= 10;
	        res += c - '0';
	        c = read();
	      } while (!isSpaceChar(c));
	      return res * sgn;
	    }

	    public int[] nextIntArray(int n) {
	      int a[] = new int[n];
	      for (int i = 0; i < n; i++) {
	        a[i] = nextInt();
	      }
	      return a;
	    }

	    public String readString() {
	      int c = read();
	      while (isSpaceChar(c)) {
	        c = read();
	      }
	      StringBuilder res = new StringBuilder();
	      do {
	        res.appendCodePoint(c);
	        c = read();
	      } while (!isSpaceChar(c));
	      return res.toString();
	    }

	    public String nextLine() {
	      int c = read();
	      while (isSpaceChar(c))
	        c = read();
	      StringBuilder res = new StringBuilder();
	      do {
	        res.appendCodePoint(c);
	        c = read();
	      } while (!isEndOfLine(c));
	      return res.toString();
	    }

	    public boolean isSpaceChar(int c) {
	      return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
	    }

	    private boolean isEndOfLine(int c) {
	      return c == '\n' || c == '\r' || c == -1;
	    }
	}
   	public static class pair implements Comparable<pair>
    {
        int first;
        int second;
        public pair(int a,int b)
        {
            this.first = a;
            this.second = b;
        }
        public int compareTo(pair u)
        {
            return (u.first - u.second) - (first - second);
        }
    }
    public static long gcd(long a,long b)
    {
        if(b == 0)
            return a;
        return gcd(b,a%b);
    }
    public static ArrayList<Integer> sieve(int[] lps,int n)
	{
		ArrayList<Integer> arr = new ArrayList<>();
		for(int i = 2;i <= n;i++)
		{
			if(lps[i] == 0)
			{
				lps[i] = i;
				arr.add(i);
			}
			for(int j = 0;j < arr.size() && arr.get(j) <= lps[i] && i*arr.get(j) <= n;j++)
				lps[i*arr.get(j)] = arr.get(j);
		}
		return arr;
	}
 	public static void main(String[] args) throws Exception
    {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        PrintWriter out = new PrintWriter(System.out);
        int n = Integer.parseInt(br.readLine());
        ArrayList<Integer> x = new ArrayList<>();
        ArrayList<Integer> y = new ArrayList<>();
        if(n == 0)	
        	return;
        x.add(1);
        y.add(1);
        int max = 1;
        for(int i = 1; i < n; i++)
        {
        	int p = x.get(i - 1);
        	int q = y.get(i - 1);
        	if(i % 2 != 0)
        	{
        		x.add(p);
        		y.add(q + 1);
        	}
        	else
        	{
        		x.add(p + 1);
        		y.add(q);
        	}
        	if(x.get(x.size() - 1) > max)
        		max = x.get(x.size() - 1);
        	if(y.get(y.size() - 1) > max)
        		max = y.get(y.size() - 1);
        }
        out.println(max);
        for(int i = 0; i < n; i++)
        {
        	out.println(x.get(i) + " " + y.get(i));
        }
       	out.close(); 
    }
}